scholarly journals Seemingly Unrelated Regression Spatial Autoregressive Bayesian Modeling on Heteroscedasticity Case

2021 ◽  
Vol 2123 (1) ◽  
pp. 012047
Author(s):  
Adiatma
Keyword(s):  
Spatial Data ◽  
Bayesian Modeling ◽  
Autoregressive Model ◽  
Prior Distribution ◽  
Bayesian Method ◽  
Seemingly Unrelated Regression ◽  
Regression Equations ◽  
Spatial Autoregressive Model ◽  
Unrelated Regression ◽  
Spatial Autoregressive

Abstract The phenomenon encountered occasionally on complications involving spatial data, is that there is a tendency of heteroscedasticity since every region has distinct characteristics. Thus, it requires the approach which is more appropriate with the problem by using the Bayesian method. Bayesian method on spatial autoregressive model to contend the heteroscedasticity by applying prior distribution on variance parameter of error. To detect heteroscedasticity, it is shown from several responses correlating with the predictors. The method abled to estimate some responses is Seemingly Unrelated Regression (SUR). SUR is an econometrics model that used to be being utilized in solving some regression equations in which of them has their own parameter and appears to be uncorrelated. However, by correlation of error in differential equations, the correlation would occur among them. With the condition of the Bayesian SUR spatial autoregressive model, it is able to overcome heteroscedasticity cases from the vision of spatial. Further, the model involves four kinds of parameter priors’ distributions estimated by using the process of MCMC.

scholarly journals Bayesian Estimation of Partially Linear Additive Spatial Autoregressive Models with P-Splines

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhiyong Chen ◽  
Minghui Chen ◽  
Guodong Xing
Keyword(s):  
Spatial Data ◽  
Autoregressive Model ◽  
Estimation Method ◽  
Additive Model ◽  
Housing Price ◽  
Nonlinear Effects ◽  
Spatial Autoregressive Model ◽  
Unknown Parameters ◽  
Partially Linear ◽  
Spatial Autoregressive

In this paper, we aim to develop a partially linear additive spatial autoregressive model (PLASARM), which is a generalization of the partially linear additive model and spatial autoregressive model. It can be used to simultaneously evaluate the linear and nonlinear effects of the covariates on the response for spatial data. To estimate the unknown parameters and approximate nonparametric functions by Bayesian P-splines, we develop a Bayesian Markov Chain Monte Carlo approach to estimate the PLASARM and design a Gibbs sampler to explore the joint posterior distributions of unknown parameters. Furthermore, we illustrate the performance of the proposed model and estimation method by a simulation study and analysis of Chinese housing price data.

scholarly journals Variable Selection for the Spatial Autoregressive Model with Autoregressive Disturbances

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1448
Author(s):  
Xuan Liu ◽  
Jianbao Chen
Keyword(s):  
Variable Selection ◽  
Autoregressive Model ◽  
Rapid Development ◽  
Heterogeneous Data ◽  
Spatial Effect ◽  
Spatial Effects ◽  
Spatial Autoregressive Model ◽  
Monte Carlo Studies ◽  
Spatial Autoregressive ◽  
Theoretical Results

Along with the rapid development of the geographic information system, high-dimensional spatial heterogeneous data has emerged bringing theoretical and computational challenges to statistical modeling and analysis. As a result, effective dimensionality reduction and spatial effect recognition has become very important. This paper focuses on variable selection in the spatial autoregressive model with autoregressive disturbances (SARAR) which contains a more comprehensive spatial effect. The variable selection procedure is presented by using the so-called penalized quasi-likelihood approach. Under suitable regular conditions, we obtain the rate of convergence and the asymptotic normality of the estimators. The theoretical results ensure that the proposed method can effectively identify spatial effects of dependent variables, find spatial heterogeneity in error terms, reduce the dimension, and estimate unknown parameters simultaneously. Based on step-by-step transformation, a feasible iterative algorithm is developed to realize spatial effect identification, variable selection, and parameter estimation. In the setting of finite samples, Monte Carlo studies and real data analysis demonstrate that the proposed penalized method performs well and is consistent with the theoretical results.

scholarly journals Estimation of Partially Specified Spatial Autoregressive Model

2014 ◽  
Vol 2 (3) ◽  
pp. 226-235
Author(s):  
Yuanqing Zhang
Keyword(s):  
Autoregressive Model ◽  
Instrumental Variable ◽  
Error Term ◽  
Sufficient Conditions ◽  
Spatial Autoregressive Model ◽  
Dimensional Parameter ◽  
Instrumental Variable Estimation ◽  
Weighting Matrix ◽  
Finite Dimensional ◽  
Spatial Autoregressive

Abstract In this paper, we study estimation of a partially specified spatial autoregressive model with heteroskedasticity error term. Under the assumption of exogenous regressors and exogenous spatial weighting matrix, we propose an instrumental variable estimation. Under some sufficient conditions, we show that the proposed estimator for the finite dimensional parameter is root-n consistent and asymptotically normally distributed and the proposed estimator for the unknown function is consistent and also asymptotically distributed though at a rate slower than root-n. Monte Carlo simulations verify our theory and the results suggest that the proposed method has some practical value.

A Note on Small Sample Properties of Estimators in a First-Order Spatial Autoregressive Model

1982 ◽  
Vol 14 (8) ◽  
pp. 1023-1030 ◽  
Author(s):  
L Anselin
Keyword(s):  
Monte Carlo Simulation ◽  
Autoregressive Model ◽  
Ad Hoc ◽  
Simulation Experiment ◽  
Small Sample ◽  
Bayesian Estimator ◽  
Spatial Autoregressive Model ◽  
First Order ◽  
Small Sample Properties ◽  
Spatial Autoregressive

This note considers a Bayesian estimator and an ad hoc procedure for the parameters of a first-order spatial autoregressive model. The approaches are derived, and their small sample properties compared by means of a Monte Carlo simulation experiment.

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